Drawing graph of correlation coefficients in Matlab

Question

In Matlab, I have an n^2 x n^2 matrix Corr_M containing the Pearson correlation coefficients between all entries of a set of n x n matrix M, such that Corr_M(i,j) is the correlation coefficient between M(i) and M(j) for some M in the set. Note that Corr_M is symmetric.

I would like to graph Corr_M by showing links between different entries of M, where the link between M(i) and M(j) is colored, say, red if Corr_M(i,j) is positive and blue if it is negative. The thickness of the link indicates how strong the correlation is (preferably where links being 0.1 apart, perhaps even smaller, are distinguishable).

For a 3 x 3 M this could look like the following:

Not all entries will be connected, as many of them are not correlated (so a correlation coefficient of zero will not result in a link being shown). Note that self-correlations are not shown. Instances such as the one seen in the bottom row, where a naive implementation might simply place one line on top of the other, are problematic, but such a naive implementation is very welcome still.

Is there a standard way of doing this, perhaps with some of the in-built graph-theoretic functions of Matlab (which I, unfortunately, do not know the scope of)?

If there isn't, then how can I implement this?

Answer 1

You can try the graph object in Matlab. The following example assumes that your Corr_M is a nxn matrix (see below):

% set the source of the lines:
s = repelem(1:n-1,n-1:-1:1);
% set the target of the lines:
t = nonzeros(triu(repmat(2:n,n-1,1)).').';
Corr_M(~Corr_M) = nan; % replace zero weights with nan
weights = nonzeros(tril(Corr_M,-1));
% create the graph object:
G = graph(s,t,weights,n);
% mark the lines to remove from the graph:
threshold = 0.4; %  minimum correlation to plot
line_to_remove = isnan(weights) | abs(weights)<threshold;
% remove the lines from the graph:
G = G.rmedge(find(line_to_remove)); %#ok<FNDSB>
% plot it:
p = plot(G); % for labeling the lines uncomment add: 'EdgeLabel',G.Edges.Weight
p.NodeColor = 'k';
% color positive in blue and negative in red:
p.EdgeColor = [G.Edges.Weight<0.' zeros(numel(G.Edges.Weight),1) G.Edges.Weight>0.'];
% set the thickness of the lines:
p.LineWidth = abs(G.Edges.Weight)*5;
axis off

If you want the nodes to be in a grid, then you need to set the XData and YData properties of the plotted graph.

% get the grid coordinates for all nodes
[x,y] = ndgrid(1:ceil(sqrt(n)),1:ceil(sqrt(n)));
x = x(:);
y = y(:);
% set the nodes in a 'grid' structure
p.XData = x(1:n);
p.YData = y(1:n);
axis ij % flip the plot so it will be orderd like in a matrix

with n = 9 it will look like this (using some random Corr_M):

Corr_M =
            0            0            0            0            0            0            0            0            0
       0.9504            0            0            0            0            0            0            0            0
     0.016371      0.24554            0            0            0            0            0            0            0
     -0.11467     -0.19375     -0.30812            0            0            0            0            0            0
     -0.01241    -0.090871      0.74444      0.34121            0            0            0            0            0
     -0.21623      0.36844      0.83935     -0.83914     -0.12302            0            0            0            0
    -0.011428   -0.0077929     -0.26243     -0.98249     -0.57997      0.55024            0            0            0
      0.64245      -0.6027      0.51424      0.62646      0.32854      0.18052     0.055688            0            0
     -0.51699      0.47885      0.44677      0.18128      0.26819     -0.67849    -0.034057      0.28652            0

One of the problems with graph plots is the very small text that you can't change. If this important, read the following suggestion.